A parameterized shift-splitting preconditioner for saddle point problems.

Recently, Chen and Ma [A generalized shift-splitting preconditioner for saddle point problems, Applied Mathematics Letters, 43 (2015) 49-55] introduced a generalized shift-splitting preconditioner for saddle point problems with symmetric positive definite (1,1)-block. In this paper, I establish a parameterized shift-splitting preconditioner for solving the large sparse augmented systems of linear equations. Furthermore, the preconditioner is based on the parameterized shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration, which has the intersection with the generalized shift-splitting preconditioner.

Permutation transformations of tensors with an application.

The permutation transformation of tensors is introduced and its basic properties are discussed. The invariance under permutation transformations is studied for some important structure tensors such as symmetric tensors, positive definite (positive semidefinite) tensors, -tensors, -tensors, Hankel tensors, -tensors, -tensors and -tensors. Finally, as an application of permutation transformations of tensors, the canonical form theorem of tensors is given.

The evolution of optimal resource allocation and mating systems in hermaphroditic perennial plants.

By incorporating the effects of inbreeding depression (ID) on both juveniles and adults survivorship, we developed a new theoretical model for hermaphroditic perennial plants. Our model showed that the effect of the selfing rate on the evolutionarily stable strategy (ESS) reproductive allocation depends on three parameters: (1) the self-fertilized juvenile relative survivorship (SFJRS), (2) the self-fertilized adult relative survivorship (SFARS) and (3) the growth rate of self-fertilized adult, where the SFJRS is the survivorship of self-fertilized juveniles divided by the survivorship of outcrossed juveniles, and likewise for the SFARS. However, the ESS sex allocation decreases as the selfing rate increases.

Collective punishment is more effective than collective reward for promoting cooperation.

Collective punishment and reward are usually regarded as two potential mechanisms to explain the evolution of cooperation. Both scenarios, however, seem problematic to understand cooperative behavior, because they can raise the second-order free-rider problem and many organisms are not able to discriminate less cooperating individuals. Even though they have been proved to increase cooperation, there has been a debate about which one being more effective.

The shift between the Red Queen and the Red King effects in mutualisms.

Interspecific mutualisms consist of partners trading services that yield common benefits to both species. Until now, understanding how the payoffs from mutualistic cooperation are allocated among the participants has been problematic. Two hypotheses have been proposed to resolve this problem.

Evolutionary stability in the asymmetric volunteer's dilemma.

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer's dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.

Resource elasticity of offspring survival and the optimal evolution of sex ratios.

The fitness of any organisms includes the survival and reproductive rate of adults and the survival of their offspring. Environmental selection pressures might not affect these two aspects of an organism equally. Assuming that an organism first allocates its limited resources to maintain its survival under environmental selection pressure, our model, based on the evolutionarily stable strategy theory, surprisingly shows that the sex ratio is greatly affected by the environmental pressure intensity and by the reproductive resource elasticity of offspring survival.

[Evolutionary stability analysis of asymmetric hawk-dove game considering the impact of common resource].

Explaining the evolution of cooperation remains one of the important problems in both biology and social science. Classical theories mainly based on an assumption that cooperative players are symmetrically interacted. However, almost all the well-studied systems showed that cooperative players are in fact asymmetrically interacted and that asymmetric interaction might greatly affect cooperation behavior of the involved players.

Asymmetric interaction will facilitate the evolution of cooperation.

Explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. The classical theories of cooperation suggest that cooperation equilibrium or evolutionary stable strategy between partners can be maintained through genetic similarity or reciprocity relatedness. These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction.